Andone, 49, who was sacked by United Arab Emirates champions Al Ahli six games into the season in November, signed an 18-month contract with the 31-times Bulgarian champions.
"It's a big honour for me," Andone told a news conference at CSKA's Bulgarska Armiya stadium. "I know a lot about CSKA, they're really a big club.
"We've talked about CSKA's goals and I agreed," he said. "Our main target will be to win the league title and play in the Champions League next season.
"It's achievable and I hope that soon top clubs will come to play at this stadium."
Luboslav Penev resigned as CSKA coach on Wednesday, after failing to offer a guarantee that he could take the club to the league title.
CSKA chief executive Ventsislav Zhivkov warned on Thursday that his replacement would have to win the league and cup double or face the sack.
The club, who have had nearly 30 coaching changes in the last two decades, went into the winter break second in the league standings with 31 points, four behind Litex Lovech.
CSKA were close to signing Miodrag Jesic but the deal fell through after the Serbian coach could not terminate his contract with Libyan league leaders Al-Ittihad.
Former Dinamo Bucharest coach Andone, capped 55 times by his country as a player, guided Romania's oldest club CFR Cluj to the domestic double in 2008.
